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Essentials of Game Theory

Book Description

Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them.

Table of Contents

  1. Cover
  2. Synthesis Lectures on Artificial Intelligence and Machine Learning
  3. Copyright
  4. Title Page
  5. Dedication
  6. Contents
  7. Credits and Acknowledgments
  8. Preface
  9. 1. Games in Normal Form
    1. 1.1 Example: The TCP User’s Game
    2. 1.2 Definition of Games in Normal Form
    3. 1.3 More Examples of Normal-Form Games
      1. 1.3.1 Prisoner’s Dilemma
      2. 1.3.2 Common-payoff Games
      3. 1.3.3 Zero-sum Games
      4. 1.3.4 Battle of the Sexes
    4. 1.4 Strategies in Normal-form Games
  10. 2. Analyzing Games: From Optimality To Equilibrium
    1. 2.1 Pareto optimality
    2. 2.2 Defining Best Response and Nash Equilibrium
    3. 2.3 Finding Nash Equilibria
  11. 3. Further Solution Concepts for Normal-Form Games
    1. 3.1 Maxmin and Minmax Strategies
    2. 3.2 Minimax Regret
    3. 3.3 Removal of Dominated Strategies
    4. 3.4 Rationalizability
    5. 3.5 Correlated Equilibrium
    6. 3.6 Trembling-Hand Perfect Equilibrium
    7. 3.7 E-Nash Equilibrium
    8. 3.8 Evolutionarily Stable Strategies
  12. 4. Games With Sequential Actions: The Perfect-information Extensive Form
    1. 4.1 Definition
    2. 4.2 Strategies and Equilibria
    3. 4.3 Subgame-Perfect Equilibrium
    4. 4.4 Backward Induction
  13. 5. Generalizing the Extensive Form: Imperfect-Information Games
    1. 5.1 Definition
    2. 5.2 Strategies and Equilibria
    3. 5.3 Sequential Equilibrium
  14. 6. Repeated and Stochastic Games
    1. 6.1 Finitely Repeated Games
    2. 6.2 Infinitely Repeated Games
    3. 6.3 Stochastic Games
      1. 6.3.1 Definition
      2. 6.3.2 Strategies and Equilibria
  15. 7. Uncertainty About Payoffs: Bayesian Games
    1. 7.1 Definition
      1. 7.1.1 Information Sets
      2. 7.1.2 Extensive Form with Chance Moves
      3. 7.1.3 Epistemic Types
    2. 7.2 Strategies and Equilibria
    3. 7.3 Computing Equilibria
    4. 7.4 Ex-post Equilibria
  16. 8. Coalitional Game Theory
    1. 8.1 Coalitional Games with Transferable Utility
    2. 8.2 Classes of Coalitional Games
    3. 8.3 Analyzing Coalitional Games
      1. 8.3.1 The Shapley Value
      2. 8.3.2 The Core
  17. History and References
  18. References
  19. Index